## How can you prove that a function has no closed form integral?

In the past, I’ve come across statements along the lines of “function $f(x)$ has no closed form integral”, which I assume means that there is no combination of the operations: addition/subtraction multiplication/division raising to powers and roots trigonometric functions exponential functions logarithmic functions which when differentiated gives the function $f(x)$. I’ve heard this said about … Read more